Question

How do I know if these equations are polynomials???? I’m so confused. (Photos attached)

Answer 1

It's essential you understand precisely what "polynomial" means.  
Characteristics of polynomials: 
1) All powers of x are zero or positive integers.  This eliminates any powers of x which show up in the denominator of any term.  No square or cube roots, for example.
2) Coefficients are real numbers, but need not be integer.
3) Generally you'll have a function name (such as "y") on the left of the " = " sign and ONLY powers of the independent variable (such as "x") on the right side.

In the list given, I see 2 polynomials.  In 6 + w appears the first power of w; that integer power is 1.  In the second I see y with the fractional exponent (1/3); this expression is NOT a polynomial.  In the third, we have the same situation as in the first (6+w); this is a poly.  In the fourth and last expression, I see a mixture of x and y.  y = 2x^4 would be poly, but 2x^4 - y would not.